. Rectilinear Vortices

A rectilinear vortex is a vortex tube whose generators are perpendicular to the plane of motion. Now, let us have a closer look at some aspects of two-dimensional vortex motion. We know that the circulation

Vortex tube

in an infinitesimal plane circuit is proportional to the area of the circuit. In a two-dimensional motion the vorticity vector Z at any point P, which is perpendicular to the plane of motion and whose magnitude is equal to the limit of the ratio of the circulation is an infinitesimal circuit embracing P to the area of the circuit. That is, the vorticity vector is by definition perpendicular to the plane of the motion, so that the vortex lines are straight and parallel. All vortex tubes are therefore cylinders whose generators are perpendicular to the plane of motion. Such vortices are known as rectilinear vortices. For our discussions in this section, let us consider the fluid between parallel plates at unit distance apart and parallel to the plane of the motion, which is half-way between them.